Failure inference from a marker process based on a bivariate Wiener model

Area of Science:

• Biostatistics
• Survival Analysis
• Stochastic Processes

Background:

• Existing models often link failure times to observable markers, which can be unrealistic.
• Joint models for marker evolution and failure can involve complex calculations.
• A need exists for more realistic and computationally tractable models for time-varying covariates and failure times.

Purpose of the Study:

• To develop a novel statistical model for failure times influenced by unobservable, time-varying covariates.
• To provide a model that simplifies the calculation of key characteristics like marginal failure time distributions.
• To offer a flexible framework for analyzing complex data structures in survival analysis.

Main Methods:

• Utilized a bivariate Wiener process, with one component for an observable marker and a second latent component for failure time.
• Failure is modeled as the latent component crossing a threshold.
• Developed methods for parametric and predictive inference, including model checking and an extension for composite markers.

Main Results:

• The proposed bivariate Wiener process model yields simpler expressions for failure time characteristics.
• The model is demonstrated to be easily fitted to common data types, including censored cases.
• An extension allows for the integration of multiple candidate markers into a composite marker.

Conclusions:

• The bivariate Wiener process model offers a computationally efficient and realistic approach to analyzing failure times with latent covariates.
• The model's flexibility and ease of fitting make it suitable for various applications in biostatistics and survival analysis.
• The methodology is validated through simulation and a real-world case study.